We created an individual-based model of termite tunnel excavation from rules derived from experimental data. We specifically avoided invoking the pheromone gradients used in previous models of termite construction. Tunnel orientation emerges as the aggregate of individual excavator’s dead reckoning combined with their stigmergic response to the relief of tunnel wall profiles. Tunnel width and branching are governed by a balance between excavated soil moving back from the burgeoning tunnel tip being plastered along the tunnel walls and soil being removed from tunnel walls in response to queuing and the flow rate of individuals through the tunnel. Tunnel patterns generated by the model were compared with empirical termite tunnels.